Normality Calculator

Normality N = equivalents ÷ volume, where equivalents = moles × n factor = molarity × n factor × volume

N

Normality — equivalents of solute per litre of solution. It is the concentration unit titrations are written in, and the one that depends on which reaction the substance is taking part in

eq

The number of equivalents, the quantity all three routes arrive at. One equivalent is one mole of the reacting unit — of protons, of electrons, of charge

n

The n factor: how many protons or electrons one formula unit transfers in this particular reaction. It has no units, it is between 1 and 10 here, and it is the one number the page cannot work out for you

M

Molarity, the ordinary concentration in moles per litre. Multiplying it by the n factor is the whole of the conversion to normality

V

The volume of solution in litres. It appears twice over: once dividing the equivalents to give normality, and once inside the solution route that produced those equivalents

Use it wherever a titration is written in normality rather than molarity, which is most of classical volumetric analysis. The reason the unit exists is that one millilitre of 1 N acid neutralises one milliequivalent of base, whatever the acid is — the n factor has already absorbed the difference, so the arithmetic of a titration becomes volume times normality with nothing else to remember. It is also the unit clinical chemistry reports in, where the equivalent is the charge rather than the molecule and milliequivalents per litre is how serum electrolytes are quoted. If what you want is moles per litre with no reaction-dependent number in it, the molarity page does that directly.

1. A dibasic acid, where N and M are not the same number

   1. The substance transfers two protons, so the n factor is 2
   2. Equivalents: 0.5 mol × 2 = 1 eq
   3. Normality: 1 eq ÷ 1 L = 1 N
   4. Molarity: 1 ÷ (2 × 1) = 0.5 M

   This is the pair of numbers the page exists to keep straight: the solution is 1 N and 0.5 M at the same time, and reporting one where the other was meant is out by a factor of two. The equivalents row is the pivot — everything else is that number divided by a volume, once with the n factor and once without.

2. A permanganate titration, where the factor is the reaction

   1. In acidic solution permanganate takes on five electrons, so the n factor is 5
   2. Equivalents: 0.02 mol/L × 5 × 0.025 L = 0.0025 eq
   3. Normality: 0.0025 ÷ 0.025 = 0.1 N
   4. In milliequivalents: 2.5 mEq, which is how the burette reading would be recorded

   The same 0.02 M permanganate is 0.1 N here and 0.06 N in neutral solution, where the factor is 3 — the concentration did not change, the reaction did. That is why the n factor is an input rather than something the page derives from the formula, and why the reference table below prints permanganate twice.

3. The smallest quantity the fields allow

   1. Equivalents are given directly: 0.0001 eq, the smallest the field accepts
   2. Normality: 0.0001 ÷ 100 L = 1 × 10⁻⁶ N
   3. Molarity: 0.0001 ÷ (10 × 100) = 1 × 10⁻⁷ M
   4. In milliequivalents: 0.1 mEq

   Four rows, four different scales, and not one of them reads zero — which is the whole reason the output precisions differ. The molarity row keeps seven decimals rather than six because it divides by the n factor as well as the volume, and at ten times the factor the smallest answer lands one power of ten lower. Had it been given six, this row would print 0.000000, and a solution that is a tenth of a micromole per litre would look like one that contains nothing.

The n factor is the user's to supply and the page takes it on trust. It cannot be checked against anything here, because it is a property of the reaction rather than of the substance, and a wrong one produces an answer that is wrong by exactly that factor while looking entirely plausible — this is the single largest source of error in normality calculations and no arithmetic can catch it. The reference table gives the usual values for ten common reagents, but those are recommendations for the reactions they are normally used in, not a lookup of what the substance necessarily is. Normality itself is a formal or legacy unit: the SI has no place for it, because the equivalent is not a unit but a convention about which particle is being counted, and the same solution has as many normalities as it has reactions. The three routes are checked against each other to within one percent, which catches a mistyped number but not a systematically wrong n factor applied to all of them. Temperature is not accounted for — a normality is defined at the volume the solution had when it was made, and a solution that has warmed up since then is slightly more dilute than its label. And the arithmetic assumes the solute is pure and fully dissolved, which is a statement about the sample rather than the chemistry.

What is the difference between normality and molarity?

Normality is molarity multiplied by the n factor — the number of protons or electrons one formula unit transfers in the reaction at hand. A 1 M solution of a diprotic acid is 2 N, while a 1 M solution of a monoprotic one is 1 N; the molarity is the same kind of quantity in both cases, and the normality is not. The calculator prints both, one above the other, so that the multiplication is visible on every answer rather than being something to remember. If you only know one of them and want the other, divide or multiply by the n factor.

How do I find the n factor?

Count how many protons or electrons one formula unit gives up or takes on in the reaction you are doing. Hydrochloric acid gives up one proton, so its factor is 1; sulfuric acid gives up two, so 2; phosphoric acid three. For redox, count electrons: permanganate takes five in acidic solution and three in neutral or weakly alkaline solution, and dichromate takes six. The reference table on this page lists the usual values for ten common reagents, with permanganate appearing twice because its factor is settled by the medium rather than by the formula.

What is equivalent weight?

The molar mass divided by the n factor — the mass that supplies one equivalent, in grams per equivalent. Sulfuric acid has a molar mass of 98.072 g/mol and a factor of 2, so its equivalent weight is 49.04 g/eq, and weighing out 49.04 grams and making it up to one litre gives a 1 N solution. It is the number you actually use at the balance, which is why the table prints it: the reciprocal of the n factor is not much use on its own, but the equivalent weight is what you weigh.

Why does the page ask for the n factor instead of working it out from the formula?

Because the formula does not contain the answer — the reaction does. Permanganate is KMnO4 in every titration, yet it is 5 N per mole in acid and 3 N per mole in neutral solution, and the ions are the same either way. Working the factor out would mean knowing which half-reaction is running, and that information is not in the box you type a formula into. So the page takes the factor as an input and shows you the molarity alongside, which is the check that the factor you typed is doing what you expected.

What are milliequivalents used for?

They are a thousandth of an equivalent, and they are the unit titration burettes and clinical labs are read in. One millilitre of a 1 N solution delivers one milliequivalent, which is why normality makes titration arithmetic so short: volume in millilitres times normality gives milliequivalents directly. In medicine the equivalent is the charge rather than the molecule, so serum electrolytes are quoted in milliequivalents per litre — sodium at about 140 mEq/L means 140 millimoles of positive charge, which is the quantity that matters for acid-base balance.

Can I use the calculator without knowing the volume?

Not for a concentration, which is an amount per litre and has no meaning without the litre. The volume field is required, and it is also what makes the third route work — molarity alone cannot produce equivalents without a volume to multiply by, so fill in only the molarity and the page will say there is no route to the answer. What you can do without a volume is nothing at all here: if what you have is a mass and a formula, the mole calculator turns it into moles first, and the moles come back to this page for the n factor to be applied.

• IUPAC Gold Book — normality — International Union of Pure and Applied Chemistry (IUPAC)
• IUPAC Gold Book — equivalent (equivalents) — International Union of Pure and Applied Chemistry (IUPAC)
• Standard Atomic Weights — abridged to four significant figures — Commission on Isotopic Abundances and Atomic Weights (CIAAW), IUPAC